Be greedy and learn - efficient and certified algorithms for parametrized optimal control problems

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Abstract

We consider parametrized linear-quadratic optimal control problems and provide their online-efficient solutions by combining greedy reduced basis methods and machine learning algorithms. To this end, we first extend the greedy control algorithm, which builds a reduced basis for the manifold of optimal final time adjoint states, to the setting where the objective functional consists of a penalty term measuring the deviation from a desired state and a term describing the control energy. Afterwards, we apply machine learning surrogates to accelerate the online evaluation of the reduced model. The error estimates proven for the greedy procedure are further transferred to the machine learning models and thus allow for efficient a posteriori error certification. Numerical examples highlight the potential of the proposed methodology.

Speakers from the University of Münster

Kleikamp, Hendrik

Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger)